01 Introduction modeling

Overview course

Kursziel

  • Verständnis der Modellierung zellulärer Prozesse

Methode

  • Mathematik & Computermodellierung

Themen (siehe

  • Boolesche Netzwerke
  • Differentialgleichungen & dynamische Systeme
  • Constraint-based models
  • Cellular networks
  • Stochastic systems
  • Parameter fitting
  • …

Anwendungen und Beispiele

  • Stoffwechsel/Metabolismus
  • Signaltransduktion
  • Genexpression
  • Cell cycle

Lernziele

  • wie modelliert man zelluläre Prozesse? Welche Methoden gibt es?
  • was ist ein dynamisches System?
  • was ist der Zustandsraum (state space), was sind Trajektorien?
  • was sind Feedback Loops?
  • was ist Stabilität?

Komplexität biologischer Systeme

  • incomplete knowledge

  • many components

  • roles of and interactions between components are often obscure and change over time

  • nonlinearities & feedbacks

  • multiple spatial scales ​- from organism to single molecule

  • different time-scales ​- from the human life span down to molecular kinetics, e.g. of enzyme catalysis in a fraction of a second

  • build via evolution

  • complex processes

    • often not explained from first principle
    • no understanding of behavior by intuition
    • emergent properties (more than the sum of its parts)

⇒ requirement of abstract representation

Was ist ein Model?

A model is an artificial construct in the language of mathematics that represents biological phenomenon.

Gute Modelle

  • “essentially, all models are wrong, but some are useful” G. Box
  • enable ​**insights** into processes and systems ​(that we would not be able to gain otherwise)
  • repository of knowledge - ​make sense of large number of isolated facts and observations
  • allow to make ​**predictions** and ​**extrapolations** ​(which can be tested)
  • lead to the ​formulation of new hypotheses

Models can take any form

  • model can be intuitive or very abstract
  • minimal models vs. whole cell models

Wie konstruiert man ein Modell?

Abstraction steps

  • biological system
  • mental model
  • model scheme
  • process model
  • mathematical model
  • quantitative analysis

Modellierung ist Kunst

  • requires ​**technical expertise** and ​creativity
  • nicht zu kompliziert/nicht zu einfach → richtiger Abstraktionsgrad
  • conceptualizing in modules/components/processes
  • subjective and selective procedure
  • abhängig von Fragestellung

Modelling cycle - ​model predictions → experiments (validation) → refining models

Nichtlineare Dynamik

Dynamisches System
a function describes the time-dependence of a point in a state space.
  • state - Zustand
  • state space - Zustandsraum (all possible states)
  • function - rule how state is changing over time (depending on state and possible history)

Zustand​

  • discrete / continuous
  • single state variable, or more often state vector (i.e. multiple variables define the concrete state, e.g., concentrations of metabolites)

Zustandsraum

  • entsprechend diskret/kontinuierlich
  • ein-dimensional / hoch-dimensional

Zeit/time

  • diskret/kontinuierlich

Function/rules

  • deterministisch, stochastisch
  • (description as state updates or changes in state over time)

Mögliche Fragen

  • time-evolution of the system (where do I end up depending on the start conditions)?
  • steady states (nothing is changing over time any more)?
  • which states are visited? periodic states (oscillations)?
  • stability & robustness ? (if I change a bit do I get similar results)
  • sensitivity (what is the effect of parameter changes and initial condition changes)

References

  • Herbert Sauro, Introduction to Pathway Modeling, First Edition; Chapter 4, Introduction to modelling
  • Eberhard O. Voit, A first course in Systems Biology, second edition; Chapter 1, Biological systems; Chapter 2, Introduction to mathematical modelling
  • Klipp, Liebermeister, Wierling, Kowald; Systems Biology - A Textbook, Second Edition; Part I, Introduction to Systems Biology

TODO add figures (coming soon)

TODO better formulations & English/German version